roughly vs approximately

roughly and approximately both are adverbs.

Word	Noun	Adjective	Verb	Adverb
roughly	No	No	No	Yes
approximately	No	No	No	Yes

As adverbs, roughly and approximately are synonyms defined as:

roughly and approximately: (of quantities) imprecise but fairly close to correct

Other synonyms of roughly include about, around, close to, just about, more or less, or so, some.

roughly (adverb)	approximately (adverb)
(of quantities) imprecise but fairly close to correct	(of quantities) imprecise but fairly close to correct
with rough motion as over a rough surface
with roughness or violence (`rough' is an informal variant for `roughly')